This school in TX has info on the IB Extended Essay in mathematics, which I thought the OP is pursuing.
There are IB schools all over the world with sample essays or rubrics.
My impression is, a topic of applied math as you described may suffice for the OP and IB requirement. Much research may be first a survey o the body of knowledge and then eventually narrowing down to a topic of investigation, following the scientific method.
https://mwschool.libguides.com/diploma/extended-essay/math-guide
But, the above does not seem to be the same as assisting with college level mathematics research, which the OP thinks they need for college admissions…